Question

Consider the reaction: X + Y -> Z. FRom the data below, determine the Rate when [X] = 0.50M and [Y] = 0.25M.

Rate (M/s) [X](M) [Y](M)

0.053 ------0.10----0.50
0.127-------0.20----0.30
1.02---------0.40----0.60
0.254-------0.20----0.60
0.509-------0.40-----0.30

Answer 1

rate of the reaction -r =K[X]^m [Y]ⁿ

m and n are orders with respect to X and Y. K is the rate constant

from experiment 2 ,   K[0.2]^m [0.3]ⁿ= 0.127     (1)

from experiment 4    K [0.2]^m [0.6]ⁿ= 0.254       (2)

Eq.2/ Eq.1 gives [2]ⁿ= 2   n=1

experiment 3    K[0.4]^m [0.6]ⁿ= 1.02       (3)

Eq.3 / Eq.2 gives [2]^m= 1,02/0.254=4, m=2

The rate becomes -r = K[ X]² [Y]¹

from experiment 1   0.053 =K[ 0.1]² [0.5]¹, K[ 0.005]

K= 0.053/0.005=10.6/M.s

The rare expression becomes -r =10.6 [X]² [Y]¹

at [X] =0.5M and Y= 0.25M rate= 10.6*[0.5]² [0.25]=0.6625 M/s